Matching procedures, related to the group structure of block-spin renorrnalization, are proposed for an optimal choice of parameter-dependent transformations. The method also allows to determine the parameter's dependence on the reduced coupling near the fixed point. Applications to linear transformations for two- and three-dimensional Ising models and twodimensional three-, four-, and five-state Potts systems are reported. With simple approximations
good estimates of critical couplings and exponents are obtained. Results for the two-dimensional spin-1/2 XY system and their possible implications, as far as an eventual transition is concerned, are discussed. Some applications to nonlinear transformations are also considered.